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Quadratic convergence for valuing American options using a penalty method. (English) Zbl 1020.91017

The authors apply penalty methods to the (one dimensional) American option pricing problem. In the discretized version of the equilvalent linear complementarity problem they determine sufficient conditions for monotone convergence of the penalty iteration. Quadratic convergence is obtained by a suitable timestep selector.
The method is applicable to more complex, multi dimensional versions of the basic problem; the authors’ computational experience is that even in cases where the sufficient condition for convergence is not satisfied, the relevant algorithm converges fastly.

MSC:

91B28 Finance etc. (MSC2000)
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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